Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Equivalence_of_categories> ?p ?o }
- Equivalence_of_categories abstract "In category theory, an abstract branch of mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are \"essentially the same\". There are numerous examples of categorical equivalences from many areas of mathematics. Establishing an equivalence involves demonstrating strong similarities between the mathematical structures concerned. In some cases, these structures may appear to be unrelated at a superficial or intuitive level, making the notion fairly powerful: it creates the opportunity to \"translate\" theorems between different kinds of mathematical structures, knowing that the essential meaning of those theorems is preserved under the translation.If a category is equivalent to the opposite (or dual) of another category then one speaks ofa duality of categories, and says that the two categories are dually equivalent.An equivalence of categories consists of a functor between the involved categories, which is required to have an \"inverse\" functor. However, in contrast to the situation common for isomorphisms in an algebraic setting, the composition of the functor and its \"inverse\" is not necessarily the identity mapping. Instead it is sufficient that each object be naturally isomorphic to its image under this composition. Thus one may describe the functors as being \"inverse up to isomorphism\". There is indeed a concept of isomorphism of categories where a strict form of inverse functor is required, but this is of much less practical use than the equivalence concept.".
- Equivalence_of_categories wikiPageID "379051".
- Equivalence_of_categories wikiPageLength "13284".
- Equivalence_of_categories wikiPageOutDegree "72".
- Equivalence_of_categories wikiPageRevisionID "665329730".
- Equivalence_of_categories wikiPageWikiLink Abelian_category.
- Equivalence_of_categories wikiPageWikiLink Additive_category.
- Equivalence_of_categories wikiPageWikiLink Adjoint_functors.
- Equivalence_of_categories wikiPageWikiLink Algebraic_geometry.
- Equivalence_of_categories wikiPageWikiLink Axiom_of_choice.
- Equivalence_of_categories wikiPageWikiLink Birkhoffs_representation_theorem.
- Equivalence_of_categories wikiPageWikiLink Boolean_algebra_(structure).
- Equivalence_of_categories wikiPageWikiLink C*-algebra.
- Equivalence_of_categories wikiPageWikiLink Cartesian_closed_category.
- Equivalence_of_categories wikiPageWikiLink Category:Adjoint_functors.
- Equivalence_of_categories wikiPageWikiLink Category:Category_theory.
- Equivalence_of_categories wikiPageWikiLink Category_(mathematics).
- Equivalence_of_categories wikiPageWikiLink Category_theory.
- Equivalence_of_categories wikiPageWikiLink Class_(set_theory).
- Equivalence_of_categories wikiPageWikiLink Cokernel.
- Equivalence_of_categories wikiPageWikiLink Commutative_ring.
- Equivalence_of_categories wikiPageWikiLink Compact_space.
- Equivalence_of_categories wikiPageWikiLink Coproduct.
- Equivalence_of_categories wikiPageWikiLink Dimension_(vector_space).
- Equivalence_of_categories wikiPageWikiLink Dual_(category_theory).
- Equivalence_of_categories wikiPageWikiLink Epimorphism.
- Equivalence_of_categories wikiPageWikiLink Equaliser_(mathematics).
- Equivalence_of_categories wikiPageWikiLink Equivalent_definitions_of_mathematical_structures.
- Equivalence_of_categories wikiPageWikiLink Essentially_surjective_functor.
- Equivalence_of_categories wikiPageWikiLink Full_and_faithful_functors.
- Equivalence_of_categories wikiPageWikiLink Functional_analysis.
- Equivalence_of_categories wikiPageWikiLink Functor.
- Equivalence_of_categories wikiPageWikiLink Gelfand_representation.
- Equivalence_of_categories wikiPageWikiLink Group_(mathematics).
- Equivalence_of_categories wikiPageWikiLink Hausdorff_space.
- Equivalence_of_categories wikiPageWikiLink If_and_only_if.
- Equivalence_of_categories wikiPageWikiLink Initial_and_terminal_objects.
- Equivalence_of_categories wikiPageWikiLink Injective_function.
- Equivalence_of_categories wikiPageWikiLink Isomorphism.
- Equivalence_of_categories wikiPageWikiLink Isomorphism_of_categories.
- Equivalence_of_categories wikiPageWikiLink Kernel_(category_theory).
- Equivalence_of_categories wikiPageWikiLink Lattice_(order).
- Equivalence_of_categories wikiPageWikiLink Limit_(category_theory).
- Equivalence_of_categories wikiPageWikiLink Mathematics.
- Equivalence_of_categories wikiPageWikiLink Matrix_(mathematics).
- Equivalence_of_categories wikiPageWikiLink Maximal_ideal.
- Equivalence_of_categories wikiPageWikiLink Monomorphism.
- Equivalence_of_categories wikiPageWikiLink Natural_transformation.
- Equivalence_of_categories wikiPageWikiLink Partial_function.
- Equivalence_of_categories wikiPageWikiLink Pointed_set.
- Equivalence_of_categories wikiPageWikiLink Pointless_topology.
- Equivalence_of_categories wikiPageWikiLink Preadditive_category.
- Equivalence_of_categories wikiPageWikiLink Prime_ideal.
- Equivalence_of_categories wikiPageWikiLink Product_(category_theory).
- Equivalence_of_categories wikiPageWikiLink Real_number.
- Equivalence_of_categories wikiPageWikiLink Regular_category.
- Equivalence_of_categories wikiPageWikiLink Set_(mathematics).
- Equivalence_of_categories wikiPageWikiLink Skeleton_(category_theory).
- Equivalence_of_categories wikiPageWikiLink Spectrum_of_a_ring.
- Equivalence_of_categories wikiPageWikiLink Stone_duality.
- Equivalence_of_categories wikiPageWikiLink Stones_representation_theorem_for_Boolean_algebras.
- Equivalence_of_categories wikiPageWikiLink Surjective_function.
- Equivalence_of_categories wikiPageWikiLink Topology.
- Equivalence_of_categories wikiPageWikiLink Topos.
- Equivalence_of_categories wikiPageWikiLink Vector_space.
- Equivalence_of_categories wikiPageWikiLinkText "Equivalence of categories".
- Equivalence_of_categories wikiPageWikiLinkText "categorical equivalence".
- Equivalence_of_categories wikiPageWikiLinkText "categorically equivalent".
- Equivalence_of_categories wikiPageWikiLinkText "contravariant equivalence".
- Equivalence_of_categories wikiPageWikiLinkText "dual equivalence".
- Equivalence_of_categories wikiPageWikiLinkText "duality of categories".
- Equivalence_of_categories wikiPageWikiLinkText "duality".
- Equivalence_of_categories wikiPageWikiLinkText "dually equivalent".
- Equivalence_of_categories wikiPageWikiLinkText "equivalence of categories".
- Equivalence_of_categories wikiPageWikiLinkText "equivalence or duality".
- Equivalence_of_categories wikiPageWikiLinkText "equivalence".
- Equivalence_of_categories wikiPageWikiLinkText "equivalences of categories".
- Equivalence_of_categories wikiPageWikiLinkText "equivalences".
- Equivalence_of_categories wikiPageWikiLinkText "equivalent as categories".
- Equivalence_of_categories wikiPageWikiLinkText "equivalent".
- Equivalence_of_categories wikiPageWikiLinkText "naturally equivalent".
- Equivalence_of_categories wikiPageWikiLinkText "numerous applications".
- Equivalence_of_categories wikiPageWikiLinkText "weak equivalences".
- Equivalence_of_categories id "Equivalence_of_categories".
- Equivalence_of_categories title "Equivalence of categories".
- Equivalence_of_categories wikiPageUsesTemplate Template:Citation_needed.
- Equivalence_of_categories wikiPageUsesTemplate Template:Cite_book.
- Equivalence_of_categories wikiPageUsesTemplate Template:More_footnotes.
- Equivalence_of_categories wikiPageUsesTemplate Template:Reflist.
- Equivalence_of_categories wikiPageUsesTemplate Template:Springer.
- Equivalence_of_categories subject Category:Adjoint_functors.
- Equivalence_of_categories subject Category:Category_theory.
- Equivalence_of_categories hypernym Relation.
- Equivalence_of_categories type Agent.
- Equivalence_of_categories type Function.
- Equivalence_of_categories type Functor.
- Equivalence_of_categories type Theory.
- Equivalence_of_categories comment "In category theory, an abstract branch of mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are \"essentially the same\". There are numerous examples of categorical equivalences from many areas of mathematics. Establishing an equivalence involves demonstrating strong similarities between the mathematical structures concerned.".
- Equivalence_of_categories label "Equivalence of categories".
- Equivalence_of_categories sameAs Q1082992.